The Motion Is Simple Harmonic with Period T, Write an Equation

Multiple Choice

the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest
position after t seconds. Also assume that the positive direction of the motion is up.An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that
- $\mathrm { a } = 10 ; \quad \mathrm { T } = 3 \pi$ seconds

A) $\mathrm { d } = - 10 \cos \left( \frac { 2 } { 3 } \pi \mathrm { t } \right)$
B) $d = - 10 \sin \left( \frac { 2 } { 3 } \pi t \right)$
C) $d = - 10 \cos \left( \frac { 2 } { 3 } t \right)$
D) $\mathrm { d } = - 3 \cos \left( \frac { 1 } { 5 } \mathrm { t } \right)$